Abstract
Context. Recent Juno observations have suggested that the heavy elements in Jupiter could be diluted throughout a large fraction of its gaseous envelope, providing a stabilising compositional gradient over an extended region of the planet. This could trigger layered semi-convection, which, in the context of giant planets more generally, may explain Saturn’s luminosity excess and play a role in causing the abnormally large radii of some hot Jupiters. In giant planet interiors, it could take the form of density staircases, which are convective layers separated by thin stably stratified interfaces. In addition, the efficiency of tidal dissipation is known to depend strongly on the planetary internal structure. Aims. We aim to study the resulting tidal dissipation when internal waves are excited in a region of layered semi-convection by tidal gravitational forcing due to other bodies (such as moons in giant planet systems, or stars in hot Jupiter systems). Methods. We adopt a local Cartesian model with a background layered density profile subjected to an imposed tidal forcing, and we compute the viscous and thermal dissipation rates numerically. We consider two sets of boundary conditions in the vertical direction: periodic boundaries and impenetrable, stress-free boundaries, with periodic conditions in the horizontal directions in each case. These models are appropriate for studying the forcing of short-wavelength tidal waves in part of a region of layered semi-convection, and in an extended envelope containing layered semi-convection, respectively. Results. We find that the rates of tidal dissipation can be enhanced in a region of layered semi-convection compared to a uniformly convective medium, where the latter corresponds with the usual assumption adopted in giant planet interior models. In particular, a region of layered semi-convection possesses a richer set of resonances, allowing enhanced dissipation for a wider range of tidal frequencies. The details of these results significantly depend on the structural properties of the layered semi-convective regions. Conclusions. Layered semi-convection could contribute towards explaining the high tidal dissipation rates observed in Jupiter and Saturn, which have not yet been fully explained by theory. Further work is required to explore the efficiency of this mechanism in global models.
Highlights
Based on astrometric measurements spanning more than a century, Lainey et al (2009, 2012, 2017) found that the rates of tidal dissipation in Jupiter and Saturn are one order of magnitude higher than previously thought
This has important astrophysical consequences since tidal interactions are a key mechanism for driving the rotational, orbital, and thermal evolution of moons and planets on very long timescales. We know that this evolution is linked to the efficiency of tidal dissipation in celestial bodies and strongly depends on their internal structures
We study for the first time the impact of layered semi-convection upon the efficiency of tidal dissipation within an idealised Cartesian model
Summary
Based on astrometric measurements spanning more than a century, Lainey et al (2009, 2012, 2017) found that the rates of tidal dissipation in Jupiter and Saturn are one order of magnitude higher than previously thought. Two tidal components are usually distinguished: the equilibrium tide, a large-scale flow induced by the quasi-hydrostatic adjustment to the gravitational potential of the perturber (such as the moons of giant planets; see Zahn 1966; Remus et al 2012), and the dynamical tide, composed of internal waves excited by the perturber (Zahn 1975; Ogilvie & Lin 2004) Their restoring forces are buoyancy and the Coriolis acceleration, they are often called gravito-inertial waves. Which provides a measure of the dissipation at low frequencies This quantity will be useful for studying how the dissipation varies with the parameters of our problem, including the properties of the background density staircase In the case of an eccentric or inclined orbit, several frequencies should instead be considered (e.g. Zahn 1966, 1977; Mathis & Le Poncin-Lafitte 2009; Ogilvie 2014)
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